%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:26:18 PM UTC 2026
% Result : Theorem 0.14s 10.62s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO266+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/10.59 % Computer : n002.cluster.edu
% 0.11/10.59 % Model : x86_64 x86_64
% 0.11/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.59 % Memory : 8046.5625MB
% 0.11/10.59 % OS : Linux 6.8.0-71-generic
% 0.11/10.59 % CPULimit : 300
% 0.11/10.59 % WCLimit : 300
% 0.11/10.59 % DateTime : Sun Sep 20 14:58:12 UTC 2026
% 0.11/10.59 % CPUTime :
% 0.14/10.60 % Drodi V4.1.1
% 0.14/10.62 % Refutation found
% 0.14/10.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/10.62 % SZS output start CNFRefutation for theBenchmark
% 0.14/10.62 fof(f1,axiom,(
% 0.14/10.62 (! [X,Y] :( unequally_directed_opposite_lines(X,Y)<=> unequally_directed_lines(X,reverse_line(Y)) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f4,axiom,(
% 0.14/10.62 (! [X,Y] :( equally_directed_lines(X,Y)<=> ~ unequally_directed_lines(X,Y) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f7,axiom,(
% 0.14/10.62 (! [L,M] :( convergent_lines(L,M)<=> ( unequally_directed_lines(L,M)& unequally_directed_opposite_lines(L,M) ) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f15,axiom,(
% 0.14/10.62 (! [L] : equally_directed_lines(L,L) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f16,axiom,(
% 0.14/10.62 (! [L,M,N] :( unequally_directed_lines(L,M)=> ( unequally_directed_lines(L,N)| unequally_directed_lines(M,N) ) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f18,axiom,(
% 0.14/10.62 (! [L,M] :( unequally_directed_lines(L,M)| unequally_directed_lines(L,reverse_line(M)) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f19,axiom,(
% 0.14/10.62 (! [L,M] :( ( unequally_directed_lines(L,M)& unequally_directed_lines(L,reverse_line(M)) )=> ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f21,axiom,(
% 0.14/10.62 (! [L,M] :~ ( left_convergent_lines(L,M)| left_convergent_lines(L,reverse_line(M)) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f37,conjecture,(
% 0.14/10.62 (! [L,M] :( unequally_directed_opposite_lines(L,M)<=> unequally_directed_opposite_lines(M,L) ) )),
% 0.14/10.62 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/10.62 fof(f38,negated_conjecture,(
% 0.14/10.62 ~((! [L,M] :( unequally_directed_opposite_lines(L,M)<=> unequally_directed_opposite_lines(M,L) ) ))),
% 0.14/10.62 inference(negated_conjecture,[status(cth)],[f37])).
% 0.14/10.62 fof(f39,plain,(
% 0.14/10.62 ![X,Y]: ((~unequally_directed_opposite_lines(X,Y)|unequally_directed_lines(X,reverse_line(Y)))&(unequally_directed_opposite_lines(X,Y)|~unequally_directed_lines(X,reverse_line(Y))))),
% 0.14/10.62 inference(NNF_transformation,[status(thm)],[f1])).
% 0.14/10.62 fof(f40,plain,(
% 0.14/10.62 (![X,Y]: (~unequally_directed_opposite_lines(X,Y)|unequally_directed_lines(X,reverse_line(Y))))&(![X,Y]: (unequally_directed_opposite_lines(X,Y)|~unequally_directed_lines(X,reverse_line(Y))))),
% 0.14/10.62 inference(miniscoping,[status(thm)],[f39])).
% 0.14/10.62 fof(f41,plain,(
% 0.14/10.62 ![X0,X1]: (~unequally_directed_opposite_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f40])).
% 0.14/10.62 fof(f42,plain,(
% 0.14/10.62 ![X0,X1]: (unequally_directed_opposite_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f40])).
% 0.14/10.62 fof(f51,plain,(
% 0.14/10.62 ![X,Y]: ((~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y))&(equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.14/10.62 inference(NNF_transformation,[status(thm)],[f4])).
% 0.14/10.62 fof(f52,plain,(
% 0.14/10.62 (![X,Y]: (~equally_directed_lines(X,Y)|~unequally_directed_lines(X,Y)))&(![X,Y]: (equally_directed_lines(X,Y)|unequally_directed_lines(X,Y)))),
% 0.14/10.62 inference(miniscoping,[status(thm)],[f51])).
% 0.14/10.62 fof(f53,plain,(
% 0.14/10.62 ![X0,X1]: (~equally_directed_lines(X0,X1)|~unequally_directed_lines(X0,X1))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f52])).
% 0.14/10.62 fof(f64,plain,(
% 0.14/10.62 ![L,M]: ((~convergent_lines(L,M)|(unequally_directed_lines(L,M)&unequally_directed_opposite_lines(L,M)))&(convergent_lines(L,M)|(~unequally_directed_lines(L,M)|~unequally_directed_opposite_lines(L,M))))),
% 0.14/10.62 inference(NNF_transformation,[status(thm)],[f7])).
% 0.14/10.62 fof(f65,plain,(
% 0.14/10.62 (![L,M]: (~convergent_lines(L,M)|(unequally_directed_lines(L,M)&unequally_directed_opposite_lines(L,M))))&(![L,M]: (convergent_lines(L,M)|(~unequally_directed_lines(L,M)|~unequally_directed_opposite_lines(L,M))))),
% 0.14/10.62 inference(miniscoping,[status(thm)],[f64])).
% 0.14/10.62 fof(f66,plain,(
% 0.14/10.62 ![X0,X1]: (~convergent_lines(X0,X1)|unequally_directed_lines(X0,X1))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f65])).
% 0.14/10.62 fof(f68,plain,(
% 0.14/10.62 ![X0,X1]: (convergent_lines(X0,X1)|~unequally_directed_lines(X0,X1)|~unequally_directed_opposite_lines(X0,X1))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f65])).
% 0.14/10.62 fof(f100,plain,(
% 0.14/10.62 ![X0]: (equally_directed_lines(X0,X0))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f15])).
% 0.14/10.62 fof(f101,plain,(
% 0.14/10.62 ![L,M,N]: (~unequally_directed_lines(L,M)|(unequally_directed_lines(L,N)|unequally_directed_lines(M,N)))),
% 0.14/10.62 inference(pre_NNF_transformation,[status(thm)],[f16])).
% 0.14/10.62 fof(f102,plain,(
% 0.14/10.62 ![L,M]: (~unequally_directed_lines(L,M)|(![N]: (unequally_directed_lines(L,N)|unequally_directed_lines(M,N))))),
% 0.14/10.62 inference(miniscoping,[status(thm)],[f101])).
% 0.14/10.62 fof(f103,plain,(
% 0.14/10.62 ![X0,X1,X2]: (~unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,X2)|unequally_directed_lines(X1,X2))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f102])).
% 0.14/10.62 fof(f110,plain,(
% 0.14/10.62 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_lines(X0,reverse_line(X1)))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/10.62 fof(f111,plain,(
% 0.14/10.62 ![L,M]: ((~unequally_directed_lines(L,M)|~unequally_directed_lines(L,reverse_line(M)))|(left_convergent_lines(L,M)|left_convergent_lines(L,reverse_line(M))))),
% 0.14/10.62 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.14/10.62 fof(f112,plain,(
% 0.14/10.62 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1)|left_convergent_lines(X0,reverse_line(X1)))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f111])).
% 0.14/10.62 fof(f117,plain,(
% 0.14/10.62 ![L,M]: (~left_convergent_lines(L,M)&~left_convergent_lines(L,reverse_line(M)))),
% 0.14/10.62 inference(pre_NNF_transformation,[status(thm)],[f21])).
% 0.14/10.62 fof(f118,plain,(
% 0.14/10.62 (![L,M]: ~left_convergent_lines(L,M))&(![L,M]: ~left_convergent_lines(L,reverse_line(M)))),
% 0.14/10.62 inference(miniscoping,[status(thm)],[f117])).
% 0.14/10.62 fof(f119,plain,(
% 0.14/10.62 ![X0,X1]: (~left_convergent_lines(X0,X1))),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f118])).
% 0.14/10.62 fof(f152,plain,(
% 0.14/10.62 (?[L,M]: (unequally_directed_opposite_lines(L,M)<~>unequally_directed_opposite_lines(M,L)))),
% 0.14/10.62 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 0.14/10.62 fof(f153,plain,(
% 0.14/10.62 ?[L,M]: ((unequally_directed_opposite_lines(L,M)|unequally_directed_opposite_lines(M,L))&(~unequally_directed_opposite_lines(L,M)|~unequally_directed_opposite_lines(M,L)))),
% 0.14/10.62 inference(NNF_transformation,[status(thm)],[f152])).
% 0.14/10.62 fof(f154,plain,(
% 0.14/10.62 ((unequally_directed_opposite_lines(sK0_skl,sK1_skl)|unequally_directed_opposite_lines(sK1_skl,sK0_skl))&(~unequally_directed_opposite_lines(sK0_skl,sK1_skl)|~unequally_directed_opposite_lines(sK1_skl,sK0_skl)))),
% 0.14/10.62 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(L,sK0_skl),skolemize(M,sK1_skl)],[f153])).
% 0.14/10.62 fof(f155,plain,(
% 0.14/10.62 unequally_directed_opposite_lines(sK0_skl,sK1_skl)|unequally_directed_opposite_lines(sK1_skl,sK0_skl)),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f154])).
% 0.14/10.62 fof(f156,plain,(
% 0.14/10.62 ~unequally_directed_opposite_lines(sK0_skl,sK1_skl)|~unequally_directed_opposite_lines(sK1_skl,sK0_skl)),
% 0.14/10.62 inference(cnf_transformation,[status(thm)],[f154])).
% 0.14/10.62 fof(f162,definition,(
% 0.14/10.62 sQ0_spl <=> (unequally_directed_opposite_lines(sK0_skl,sK1_skl))),
% 0.14/10.62 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/10.62 fof(f163,plain,(
% 0.14/10.62 unequally_directed_opposite_lines(sK0_skl,sK1_skl)|~sQ0_spl),
% 0.14/10.62 inference(component_clause,[status(thm)],[f162])).
% 0.14/10.62 fof(f164,plain,(
% 0.14/10.62 ~unequally_directed_opposite_lines(sK0_skl,sK1_skl)|sQ0_spl),
% 0.14/10.62 inference(component_clause,[status(thm)],[f162])).
% 0.14/10.62 fof(f165,definition,(
% 0.14/10.62 sQ1_spl <=> (unequally_directed_opposite_lines(sK1_skl,sK0_skl))),
% 0.14/10.62 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/10.62 fof(f166,plain,(
% 0.14/10.62 unequally_directed_opposite_lines(sK1_skl,sK0_skl)|~sQ1_spl),
% 0.14/10.62 inference(component_clause,[status(thm)],[f165])).
% 0.14/10.62 fof(f167,plain,(
% 0.14/10.62 ~unequally_directed_opposite_lines(sK1_skl,sK0_skl)|sQ1_spl),
% 0.14/10.62 inference(component_clause,[status(thm)],[f165])).
% 0.14/10.62 fof(f168,plain,(
% 0.14/10.62 sQ0_spl|sQ1_spl),
% 0.14/10.62 inference(split_clause,[status(thm)],[f155,f162,f165])).
% 0.14/10.62 fof(f169,plain,(
% 0.14/10.62 ~sQ0_spl|~sQ1_spl),
% 0.14/10.62 inference(split_clause,[status(thm)],[f156,f162,f165])).
% 0.14/10.62 fof(f175,plain,(
% 0.14/10.62 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1))|left_convergent_lines(X0,X1))),
% 0.14/10.62 inference(backward_subsumption_resolution,[status(thm)],[f112,f119])).
% 0.14/10.62 fof(f181,plain,(
% 0.14/10.62 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_lines(X0,reverse_line(X1)))),
% 0.14/10.62 inference(forward_subsumption_resolution,[status(thm)],[f175,f119])).
% 0.14/10.62 fof(f183,plain,(
% 0.14/10.62 ![X0,X1]: (~equally_directed_lines(X0,reverse_line(X1))|~unequally_directed_opposite_lines(X0,X1))),
% 0.14/10.62 inference(resolution,[status(thm)],[f53,f41])).
% 0.14/10.62 fof(f184,plain,(
% 0.14/10.62 ![X0]: (~unequally_directed_opposite_lines(reverse_line(X0),X0))),
% 0.14/10.62 inference(resolution,[status(thm)],[f183,f100])).
% 0.14/10.62 fof(f190,plain,(
% 0.14/10.62 convergent_lines(sK1_skl,sK0_skl)|~unequally_directed_lines(sK1_skl,sK0_skl)|~sQ1_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f68,f166])).
% 0.14/10.62 fof(f192,definition,(
% 0.14/10.62 sQ2_spl <=> (convergent_lines(sK1_skl,sK0_skl))),
% 0.14/10.62 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.14/10.62 fof(f193,plain,(
% 0.14/10.62 convergent_lines(sK1_skl,sK0_skl)|~sQ2_spl),
% 0.14/10.62 inference(component_clause,[status(thm)],[f192])).
% 0.14/10.62 fof(f195,definition,(
% 0.14/10.62 sQ3_spl <=> (unequally_directed_lines(sK1_skl,sK0_skl))),
% 0.14/10.62 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/10.62 fof(f197,plain,(
% 0.14/10.62 ~unequally_directed_lines(sK1_skl,sK0_skl)|sQ3_spl),
% 0.14/10.62 inference(component_clause,[status(thm)],[f195])).
% 0.14/10.62 fof(f198,plain,(
% 0.14/10.62 sQ2_spl|~sQ3_spl|~sQ1_spl),
% 0.14/10.62 inference(split_clause,[status(thm)],[f190,f192,f195,f165])).
% 0.14/10.62 fof(f201,plain,(
% 0.14/10.62 unequally_directed_lines(sK1_skl,sK0_skl)|~sQ2_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f193,f66])).
% 0.14/10.62 fof(f207,plain,(
% 0.14/10.62 ![X0,X1]: (unequally_directed_lines(X0,X1)|unequally_directed_opposite_lines(X0,X1))),
% 0.14/10.62 inference(resolution,[status(thm)],[f110,f42])).
% 0.14/10.62 fof(f210,plain,(
% 0.14/10.62 ![X0]: (unequally_directed_lines(reverse_line(X0),X0))),
% 0.14/10.62 inference(resolution,[status(thm)],[f207,f184])).
% 0.14/10.62 fof(f211,plain,(
% 0.14/10.62 unequally_directed_lines(sK0_skl,sK1_skl)|sQ0_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f207,f164])).
% 0.14/10.62 fof(f241,plain,(
% 0.14/10.62 ![X0,X1]: (~unequally_directed_lines(X0,X1)|~unequally_directed_opposite_lines(X0,X1))),
% 0.14/10.62 inference(resolution,[status(thm)],[f181,f41])).
% 0.14/10.62 fof(f248,plain,(
% 0.14/10.62 ~unequally_directed_lines(sK1_skl,sK0_skl)|~sQ1_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f241,f166])).
% 0.14/10.62 fof(f251,plain,(
% 0.14/10.62 $false|~sQ2_spl|~sQ1_spl),
% 0.14/10.62 inference(forward_subsumption_resolution,[status(thm)],[f248,f201])).
% 0.14/10.62 fof(f252,plain,(
% 0.14/10.62 ~sQ2_spl|~sQ1_spl),
% 0.14/10.62 inference(contradiction_clause,[status(thm)],[f251])).
% 0.14/10.62 fof(f253,plain,(
% 0.14/10.62 unequally_directed_lines(sK1_skl,sK0_skl)|sQ1_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f167,f207])).
% 0.14/10.62 fof(f255,plain,(
% 0.14/10.62 ~unequally_directed_lines(sK0_skl,sK1_skl)|~sQ0_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f163,f241])).
% 0.14/10.62 fof(f304,plain,(
% 0.14/10.62 ![X0]: (unequally_directed_lines(sK1_skl,X0)|unequally_directed_lines(sK0_skl,X0)|sQ1_spl)),
% 0.14/10.62 inference(resolution,[status(thm)],[f103,f253])).
% 0.14/10.62 fof(f307,plain,(
% 0.14/10.62 ![X0,X1]: (unequally_directed_lines(reverse_line(X0),X1)|unequally_directed_lines(X0,X1))),
% 0.14/10.62 inference(resolution,[status(thm)],[f103,f210])).
% 0.14/10.62 fof(f311,plain,(
% 0.14/10.62 unequally_directed_lines(sK1_skl,sK1_skl)|sQ1_spl|~sQ0_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f304,f255])).
% 0.14/10.62 fof(f319,plain,(
% 0.14/10.62 ~equally_directed_lines(sK1_skl,sK1_skl)|sQ1_spl|~sQ0_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f311,f53])).
% 0.14/10.62 fof(f321,plain,(
% 0.14/10.62 $false|sQ1_spl|~sQ0_spl),
% 0.14/10.62 inference(forward_subsumption_resolution,[status(thm)],[f319,f100])).
% 0.14/10.62 fof(f322,plain,(
% 0.14/10.62 sQ1_spl|~sQ0_spl),
% 0.14/10.62 inference(contradiction_clause,[status(thm)],[f321])).
% 0.14/10.62 fof(f328,plain,(
% 0.14/10.62 ![X0]: (unequally_directed_lines(sK0_skl,X0)|unequally_directed_lines(sK1_skl,X0)|sQ0_spl)),
% 0.14/10.62 inference(resolution,[status(thm)],[f211,f103])).
% 0.14/10.62 fof(f337,plain,(
% 0.14/10.62 ![X0,X1]: (unequally_directed_lines(X0,X1)|~equally_directed_lines(reverse_line(X0),X1))),
% 0.14/10.62 inference(resolution,[status(thm)],[f307,f53])).
% 0.14/10.62 fof(f358,plain,(
% 0.14/10.62 ![X0]: (unequally_directed_lines(X0,reverse_line(X0)))),
% 0.14/10.62 inference(resolution,[status(thm)],[f337,f100])).
% 0.14/10.62 fof(f359,plain,(
% 0.14/10.62 ![X0]: (~unequally_directed_lines(X0,X0))),
% 0.14/10.62 inference(resolution,[status(thm)],[f358,f181])).
% 0.14/10.62 fof(f364,plain,(
% 0.14/10.62 unequally_directed_lines(sK1_skl,sK0_skl)|sQ0_spl),
% 0.14/10.62 inference(resolution,[status(thm)],[f359,f328])).
% 0.14/10.62 fof(f370,plain,(
% 0.14/10.62 $false|sQ3_spl|sQ0_spl),
% 0.14/10.62 inference(forward_subsumption_resolution,[status(thm)],[f364,f197])).
% 0.14/10.62 fof(f371,plain,(
% 0.14/10.62 sQ3_spl|sQ0_spl),
% 0.14/10.62 inference(contradiction_clause,[status(thm)],[f370])).
% 0.14/10.62 fof(f372,plain,(
% 0.14/10.62 $false),
% 0.14/10.62 inference(sat_refutation,[status(thm)],[f168,f169,f198,f252,f322,f371])).
% 0.14/10.62 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/10.64 % Elapsed time: 0.041705 seconds
% 0.14/10.64 % CPU time: 0.120648 seconds
% 0.14/10.64 % Total memory used: 10.401 MB
% 0.14/10.64 % Net memory used: 10.211 MB
%------------------------------------------------------------------------------